In a DC glow discharge, the electric field is
homogeneous in the inter-electrode space. The ions striking
the cathode create secondary electrons. The electron
avalanche creates much electron that ions but electrons
being 100 times faster than ions, they drift quickly to the
anode where they are absorbed. The ions having a lot of
inertia accumulate in the inter-electrodes space, then the
number of ions accumulates increases and from an
accumulation threshold, the electric field is no longer
homogeneous while it decreases on the side anode, which
has the effect of slowing the electrons that drift towards the
anode. The process continues until the electric field at the
anode vanishes. The electrons can no longer pass freely to
the anode and are considerably slowed down. The electron
number density increases until to equal of the density of
ions. A plasma is formed near the anode. The number of
charged particles increases and the plasma extends from
the anode to the cathode. The extension of the plasma
compresses the region of strong field towards the cathode.
These phenomena continue until the creation of charged
particles is equilibrate (creation=losses). Two regions
appear, the sheath and the plasma.
The majority of electric discharge in gases (plasma) are
built upon the Boltzmann equation. In principle, the
combination of the Boltzmann equation, together with the
Maxwell equations, needed for computation of the
electromagnetic field, describes the physics of many
discharges completely provided that this set of equations is
equipped with suitable boundary conditions. In practice,
however, the Boltzmann equation is unwieldy and cannot
easily be solved without making significant simplifications.
Fluid models describe the various plasma species in
terms of average hydrodynamic quantities such as density,
momentum and energy density. These quantities are
governed by the first three moments of the Boltzmann
equation: continuity[...]

The simulation of a streamer in electric discharge is not
a new problem. Indeed, for many years authors have
proposed first the simulations in one dimensional
considering only the phenomena on the axis. These onedimensional
models remain limited and do not fully account
for the physics of discharge. This is why many authors
have focused on two-dimensional modeling. The basics of
the streamer theory were developed by Raether [1], Loeb
and Meek [2]. In their model, we explain the movement of
the discharge by that of an ionization front that propagates
within space between two electrodes. Once the discharge
is initialized, we notice that its propagation is assured
without the help of any outside agent.
Since the propagation of a streamer depends only on
its own space charge field, it can propagate towards the
cathode or towards the anode. This possibility makes it
possible to define two types of streamers: negative
streamer (also called Anode-Directed Streamers) and
positive streamer (also called Cathode-Directed Streamers)
[3].
We describe the results of numerical calculations of
negative and positive streamer propagation based on a
fully two-dimensional algorithm, which apply of fluxcorrected
scheme names ADBQUICKEST to correct and
follow the strong density gradients [4]. The development of
this algorithm has allowed us to investigate problems in
streamer propagation of considerable interest [5][19]. This
work presents the results of the algorithm application to
questions including the streamer propagation on ionization
ahead of the streamer, on applied photoionization and
ionization term, on applied field, on initial and boundary
conditions for both case of streamer.
2. Model formulation
2.1 Studied configuration
The computational domain is a cylinder of radius
R = 0.5 cm (Figure 1) [6]. This domain is limited by two
metallic electrodes parallel, planes and circular separated
by a distance d equal to 0.5 cm. The applied[...]

Atmospheric Pressure Glow Discharge controlled by
dielectric barriers (APGD) plasma sources driven by a
radio frequency (RF) power supply are developed to obtain
non-equilibrium gas discharge plasmas with large area,
high stability, uniformity and reactivity [1,2].
Recently, atmospheric pressure discharges have found
several industrial and other applications such as thin film
deposition, surface modification, ozone generation, sterilization,
bio-decontamination and others. In principle,
atmospheric pressure plasma devices can provide a crucial
advantage over low-pressure plasmas because they eliminate
complications introduced by the need for vacuum [3].
The benefit of their use lies in the fact that they offer the
possibility of low production cost without the need for
vacuum equipment. The dielectric barrier discharge (DBD)
is a common plasma source used for these applications [2].
Most of atmospheric pressure discharges are dielectric
barrier discharges (DBDs) operating in the kilohertz [4].
New sources running at much higher frequencies in the RF
range are currently under investigation [1, 2, and 3].
Model formulation
In this work, the model used to describe the kinetics of
the charged particles for the RF glow discharge at
atmospheric pressure is the second order fluid model. It is
based on the first three momentums resolution of the
Boltzmann equation. These three moments are continuity,
momentum transfer and energy equations, which are
strongly coupled with the Poisson’s equation by
considering the local electric field approximation for ions
and the local mean energy approximation for electrons.
In the present model, the transport equations derived from
the first three moments of Boltzmann's equation are written
only for electrons and positive ions
(1) e e
e
n Φ
S
t x
 
 
 
(2)
n Φ
S
t x
 

 
[...]